Control system and methods for managing a production operating under time constaraints

ABSTRACT

A control system for a production process having a plurality of operations. A plurality of time constraints exist between the operations. The control system includes a control module that defines a plurality of sub-time constraints between each two operations, generates a plurality of equations according to the time constraints and the sub-time constraints, and calculates the sub-time constraints using the equations. The control module then determines whether a status for each operation defined according to a Work-In-Process (WIP) quantity between a first operation and a checked operation and a throughput rate thereof violates sub-time constraints between the first operation and the checked operation, and releases a lot into the production line if the status for each operation satisfies the corresponding sum of the sub-time constraints.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a control system and methods forcontrolling a multiple operation production process having timeconstraints, and particularly to a control system and methods forcontrolling a production process with overlapping time constraints.

2. Description of the Related Art

Semiconductor manufacturing processes are often restricted by stringentproduction process requirements. Time constraints are one type ofproduction process requirement that should be considered during theproduction of a lot of semiconductor devices. If time constraints arebreached, for example, when the queue time of a lot exceeds process timeconstraints, the lot may need to be reworked or even scrapped. FIG. 1illustrates a production line 100 with a plurality of operations (O₁,O₂, O₃, . . . , O_(n−2), O_(n−1), O_(n)) , each of which includes atleast one process step.

Generally, there are four types of time constraints in productionprocesses: dual-operation, multi-operation, continuous, and overlappingtime constraints. The dual-operation time constraint is a basic type oftime constraint between two individual operations. FIG. 2A is aschematic diagram of a dual-operation time constraint. In FIG. 2A,production timeline 210 has two operations O₁ and O₂ with timeconstraint TC1 therebetween, that is, operations O₁ and O₂ must beperformed on a product before the expiration of a period of timeidentified by time constraint TC1. As shown in FIG. 2B, themulti-operation time constraint is an extension of the dual-operationtime constraint. In FIG. 2B, the production timeline 220 has fouroperations O₃, O₄, O₅ and O₆, with time constraint TC2 therebetween,that is, operations O₃, O₄, O₅ and O₆ must be performed on a productbefore the expiration of a period of time identified by time constraintTC2.

FIG. 2C is a schematic diagram of a continuous time constraint. Thecontinuous time constraint is a combination of time constraintscorresponding to different operation sets. In FIG. 2C, the productiontimeline 230 has three operations O₇, O₈ and O₉, with time constraintTC3 existing between operations O₇ and O₈, and with time constraint TC4existing between operations O₈ and O₉. FIG. 2D is a schematic diagram ofan overlapping time constraint. The production timeline 240 has fouroperations O₁₀, O₁₁, O₁₂ and O₁₃. An overlapping time constraint maycomprise any combination depending on process need, and may includedual-operation, multi-operation and continuous time constraints. In FIG.2D, time constraint TC5 exists between operations O₁₀ and O₁₁; timeconstraint TC6 exists between operations O₁₁ and O₁₂, and timeconstraint TC7 exists between operations O₁₂ and O₁₃. In addition, timeconstraint TC8 exists between operations O₁₀ and O₁₂ and time constraintTC9 exists between operations O₁₁ and O₁₃. In this case, time constraintTC8 overlaps time constraints TC5 and TC6, time constraint TC9 overlapstime constraints TC6 and TC7, and time constraints TC8 and TC9 overlapeach other.

Verifying the timeliness of the completion of process operations, bycomparing the various completion times with a corresponding timeconstraint, addresses timeliness concerns associated with the identifiedprocess operations. However, comparing individual operational milestones(e.g., operation completion times) against a time constraint ignoresmany of the complexities of managing the manufacture of multiple lotsthrough a production process. For example, when time constraintsoverlap, the difficulty of managing the production process across thevarious lots in process increases dramatically. With the lack of aneffective control mechanism, lots may be accepted to the production linesimply to satisfy some time constraints. Under these uncontrolledconditions, the successful completion of one or more lots may bethreatened if the lots in process encounter a bottleneck and a remnanttime-constraint window is insufficient to cover the required processtime to complete the manufacture of each respective lot.

Currently, process managers make separate lot dispatch decisions suchthat the lots avoid overlapping time constraints. This processmanagement approach simplifies the difficulty associated with dispatchdecisions. However, this process management approach ignores the dynamicnature of a manufacturing process. Specifically, this approach ignoresproduction variance between the relative operation completion timesbetween production lots. Thus, the inevitable production variancebetween production lots adds to the difficulty of achieving an optimizeddistribution of Work-In-Process (i.e., the lots) over the entireproduction schedule. Consequently, focusing on dispatch decisions aloneinevitably impacts the flexibility of the original production schedule,causing higher product variability across the various completed lots.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a controlsystem and method for managing a production process that considersoverlapping time constraints and manufacturing variance (e.g., shopfloor timing randomness) without adversely affecting the a manufacturingschedule.

It is another object of the present invention to provide a dispatchmethod that accommodates overlapping time constraints in a productionprocess.

It is another object of the present invention to provide a semiconductorproduct and manufacturing method incorporating the same.

To achieve the above objects, the control system according to thepresent invention controls a production process that includes aplurality of operations, between which a plurality of time constraintsexist. The control system includes a control module having a calculationunit and a determination unit. The calculation unit defines a pluralityof sub-time constraints between each two operations, generates aplurality of equations according thereto, and calculates the sub-timeconstraints using the equations. The determination unit then determineswhether a status for each operation, defined according to aWork-In-Process (WIP) quantity between the first operation and a checkedoperation and a throughput rate thereof, violates the sub-timeconstraints between the first operation and the checked operation, andreleases a lot into the production process (i.e., starts the productionprocess for a lot) if the status for each operation satisfies acorresponding sum of the sub-time constraints.

Further, a dispatch method accommodating overlapping time constraints ina production process is provided. First, a plurality of sub-timeconstraints between each two operations of the production line aredefined. Then, a plurality of equations are generated according to thetime constraints and the sub-time constraints. Thereafter, at least onequeue time between two operations is simulated, and the queue time isassigned to one of the sub-time constraints. Then, remnant sub-timeconstraints are calculated using the equations.

Further, a method of semiconductor product manufacturing is alsoprovided. First, a plurality of sub-time constraints between each twooperations of a production process are defined. Then, a plurality ofequations are generated according to the time constraints and thesub-time constraints. Thereafter, the sub-time constraints arecalculated using the equations. Afterward, a status for each operationis defined according to a WIP quantity between the first operation andthe checked operation of the production line and a throughput rate ofthe checked operation. Then, it is determined whether the statusviolates the sum of the time periods defined by the sub-time constraintsbetween the first operation and the checked operation. If the status foreach operation satisfies the corresponding sum of the time periodsdefined by the sub-time constraints, a lot of a semiconductor product isreleased into the production process.

BRIEF DESCRIPTION OF THE DRAWINGS

The aforementioned objects, features and advantages of this inventionwill become apparent by referring to the following detailed descriptionof the preferred embodiment with reference to the accompanying drawings,wherein:

FIG. 1 is a schematic diagram illustrating production line having aplurality of operations;

FIG. 2A is a schematic diagram of a dual-operation time constraint;

FIG. 2B is a schematic diagram of a multi-operation time constraint;

FIG. 2C is a schematic diagram of a continuous time constraint;

FIG. 2D is a schematic diagram of an overlapping time constraint;

FIG. 3 is a schematic diagram illustrating the architecture of thecontrol system for a production line with overlapping time constraintsaccording to the present invention;

FIG. 4 is a flowchart showing the operation of the calculation unit ofthe control module according to the present invention;

FIG. 5 is a flowchart showing the process of the dispatch methodaccording to the present invention;

FIG. 6 is a schematic diagram showing an example of a production linehaving four operations;

FIG. 7 is an example simulating unknown variables; and

FIG. 8 is a flowchart showing the operation of the determination unit ofthe control module according to the present invention.

DETAILED DESCRIPTION

FIG. 3 illustrates the architecture of the control system and method fora controlling a production process having overlapping time constraintsaccording to the present invention.

The control system according to the embodiment of the present inventionincludes a production line 300, a control module 310, and a database320. The production line 300 has a plurality of operations (O₁, O₂, . .. , O_(n−1), O_(n)), in which a plurality of time constraints includesdual-operation, multi-operation, continuous and overlapping timeconstraints. The database 320 records information used by the controlmodule 310, such as the process time for each operation, the timeconstraints of the production line 300, and WIP (Work-In-Process)information. It should be noted that the database 320 may exist in a MES(Manufacturing Execution System).

The control module 310 has a calculation unit 311 and a determinationunit 312. The calculation unit 311 performs a dispatching rule to cutthe overlapping time constraints into one or more sub-time constraintsbetween operations. The determination unit 312 determines whether astatus for each operation violates the sum of the periods represented bythe one or more sub-time constraints between a first operation and achecked operation, and releases a lot 330 into the production line 300if the status for each operation satisfies (i.e., is less than) thecorresponding sum of the sub-time constraints at that point in theproduction schedule. Detailed operation of the control module 310 willbe discussed later.

FIG. 4 shows the operation of the calculation unit 311 of the controlmodule 310 according to the present invention. First, in step S401, thecalculation unit 311 defines a plurality of sub-time constraints(unknown variables) between each two operations of the production line300. Then, in step S402, the calculation unit 311 generates a pluralityof equations representing functions of the sub-time constraints and thetime constraints recorded in the database 320. Thereafter, in step S403,the calculation unit 311 calculates the sub-time constraints using theequations and a dispatch method.

FIG. 5 shows the process of the dispatch method according to the presentinvention. First, instep S501, at least one queue time between twooperations is simulated. Thereafter, in step S502, the queue time isassigned to at least one of the sub-time constraints. Then, in stepS503, the remnant sub-time constraints are calculated using theequations generated by the calculation unit 311. It should be noted thatthe simulation in step S501 will stop when enough variables in theequations become known. This condition will be satisfied when the numberof unknown variables equals the difference of the number of unknownvariables and the number of equations.

FIG. 6 illustrates an example of a production line performing a processhaving four operations O₁, O₂, O₃ and O₄, in which the time constraintbetween operations O₁ and O₃ is QT1, and the time constraint betweenoperations O₂ and O₄ is QT2. First, the calculation unit 311 definesmaximum time periods x, y and z corresponding to the sub-timeconstraints between operations O₁ and O₂, O₂ and O₃, and O₃ and O₄,respectively. Thus, two equations are generated as follows:QT1=x+y  (Eq. 1)QT2=y+z  (Eq. 2)

Note that time constraints, QT1 and QT2 do not necessarily encompass theprocess time for operations O₁, O₂, O₃, and O₄. In addition, it shouldbe understood that equations 1 and 2 above represent the maximumacceptable time period between the completion of defined productionprocess operations. Actual time periods x, y and z can vary and willchange dynamically in accordance with production line timing variance.Consequently, time constraints QT1 and QT2 will be satisfied as long asthe respective sums in equations 1 and 2 do not exceed the periodassociated with each constraint in the database 320.

In addition to time periods x, y and z, the calculation unit 311 alsodefines x′, y′ and z′, the actual queue time of a specific lot betweenoperations O₁ and O₂, O₂ and O₃, and O₃ and O₄, respectively. Thus, alot can only be processed by operation O₁ without rework or scrap if thefollowing equations are satisfied.x′<x  (Eq. 3)y′<y  (Eq. 4)z′<z  (Eq. 5)

The above equations 3˜5 can be simplified using equations 1 and 2 toprovide equations 6˜8 below.x′<x  (Eq. 6)x′+y′<x+y=QT1  (Eq. 7)x′+y′+z′<x+y+z=x+QT2  (Eq. 8)

In this case, since there are three unknown variables (time periods x, yand z) and two known equations (equations 1 and 2), the queue timebetween operations O₁ and O₂ (i.e., x′) can be simulated and assigned totime period x. Once time period x is known, time periods y and z can beestimated using equations 7 and 8.

FIG. 7 is an example of simulated unknown variables. In the example, ifQT1 is 6 hours, QT2 is 8 hours, the process time (p) of operation O₂ is0.5 hour/lot, the process time of operation O₃ is 1 hour/lot, theinitial queuing WIP between operations O₁ and O₂ is 4 lots, and queuingWIP between operations O₂ and O₃ is 3 lots. After 2 hours (4 lotsprocessed by operation O₂, and 2 lots by operation O₃), the queued lotsbetween operations O₂ and O₃ become 5 lots. Since x′=2=4*0.5 and x′ isassigned to x, the time periods y and z can be estimated using equations7 and 8, which result in y=4 and z=4. The use of the ESTIMATED RESULT(time periods) will discussed later.

FIG. 8 shows the operation of the determination unit 312 of the controlmodule 310 according to the present invention. First, in step S801, thedetermination unit 312 defines a status for each operation according toLittle's law as follows:S=WIP(o ₁ , o _(n))/WPH(o _(n)),  (Eq. 9)where S is the status of a checked operation, WIP(o₁, o_(n)) is theamount of WIP between the first operation O₁ and the checked operationO_(n), and WPH(o_(n)) is the throughput rate of the checked operationO_(n), in which WPH(o_(n)) equals the reciprocal of the process time ofthe checked operation O_(n).

In accordance with equation 9, “x′”, “x′+y′”, and “x′+y′+z′” can beestimated as follows:S _(O) ₂ =x′=WIP(o ₁ , o ₂)/WPH(o ₂)  (Eq. 10)S _(O) ₃ =x′+y′=WIP(o ₁ , o ₃)/WPH(o ₃)  (Eq. 11)S _(O) ₄ =x′+y′+z′=WIP(o ₁ , o ₄)/WPH(o ₄)  (Eq. 12)

It should be noted that the status for each operation can furtherconsider a process time for each operation between the first operationand the checked operation. If process time for operation O₂ isconsidered, equation 9 becomes:S=(WIP(o ₁ , o _(n))/WPH(o _(n)))−PT(o ₂ , o _(n−1)),  (Eq. 13)where S is the status of the checked operation, WIP(o₁, o_(n)) is theamount of WIP between the first operation, O₁, and the checkedoperation, O_(n), WPH(o_(n)) is the throughput rate of the checkedoperation, O_(n), and PT(o₂, o_(n−1)) is the total process time ofoperations between the first operation and the subsequent checkedoperation (o₂˜o_(n−1)) except that process time attributed to the firstoperation O₁ and the checked operation O_(n).

Similarly, equations 10, 11 and 12 can be modified as follows:S _(O) ₂ =x′=WIP(o ₁ , o ₂)/WPH(o ₂)  (Eq. 14)S _(O) ₃ =x′+Y′=(WIP(o ₁ , o ₃)/WPH(o ₃))−PT(o ₂ , o ₂)  (Eq. 15)S _(O) ₄ =x′+y′+z′=(WIP(o ₁ , o ₄)/WPH(o ₄))−PT(o ₂ , o ₃)  (Eq. 16)

Then, in step S802, the determination unit 312 determines whether thestatus for each operation violates the sum of the time periodsassociated with the sub-time constraints between the first operation andthe checked operation. That is, the determination unit 312 determineswhether S_(O) ₂ is equal to or less than x, S_(O) ₃ is equal to or lessthan x+y, and S_(O) ₄ is equal to or less than x+y+z.

If any status violates its corresponding constraint (the sum of theperiods associated with the sub-time constraints, represented by thelogic branch labeled, “Yes” exiting step S803), in step S804, a lot of asemiconductor product waits outside the production line 300, and theflow returns to step S802. Otherwise, when a status meets itscorresponding constraint (represented by the logical branch labeled,“No” in step S803), in step S805, the lot is released into theproduction line 300, and the production process is followed tomanufacture the semiconductor product. In the case of FIG. 7, the lot isnot released into the production line since S_(O) ₃ =(WIP(o₁,o₃)/WPH(o₃))−PT(o₂, o₂)=((4+3)/1)−0.5=6.5 is greater than 6=(x+y).

As a result, the control system and method for controlling a productionprocess operating under time constraints according to the presentinvention can minimize fabrication variability and rework rate acrossproducts lots by taking advantage of production line timing variancebetween production operations and avoiding the practice of focusing onlyon overlapping time constraints when making dispatch decisionsthroughout the production process.

The methods and system of the present invention, or certain aspects orportions thereof, may take the form of program code (i.e., executableinstructions) embodied in tangible media, such as floppy diskettes,CD-ROMS, hard drives, or any other machine-readable storage medium,wherein, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing theinvention. The methods and apparatus of the present invention may alsobe embodied in the form of program code transmitted over sometransmission medium, such as electrical wiring or cabling, through fiberoptics, or via any other form of transmission, wherein, when the programcode is received and loaded into and executed by a machine, such as acomputer, the machine becomes an apparatus for practicing the invention.When implemented on a general-purpose processor, the program codecombines with the processor to provide a unique apparatus that operatesanalogously to application specific logic circuits.

Although the present invention has been described in its preferredembodiments, it is not intended to limit the invention to the preciseembodiments disclosed herein. Those who are skilled in this technologycan still make various alterations and modifications without departingfrom the scope and spirit of this invention. Therefore, the scope of thepresent invention shall be defined and protected by the following claimsand their equivalents.

1. A control system for managing a production schedule having timeconstraints that define a maximum elapsed time between operations,comprising: a calculation unit configured to define a plurality ofsub-time constraints between each two operations of the productionschedule, generate a plurality of equations representing functions ofthe time constraints and the sub-time constraints, and calculate a valuefor the sub-time constraints with the equations; and a determinationunit configured to define a status for each operation according to aWork-In-Process (WIP) quantity between a first operation and a checkedoperation of the production line and a throughput rate of the checkedoperation, check whether the status violates any of the sub-timeconstraints between the first operation and the checked operation, andrelease a lot into the production line if the status for each operationsatisfies the corresponding sum of the sub-time constraints.
 2. Thecontrol system as claimed in claim 1 wherein the calculation unitfurther simulates at least one queue time between two operations, andassigns the queue time to one of the sub-time constraints, therebyobtaining a remnant sub-time constraint.
 3. The control system asclaimed in claim 1 wherein the status is defined as follows:S=WIP(o ₁ ,o _(n))/WPH(o _(n)), wherein S is the status of a checkedoperation (O_(n)), WIP(o₁,o_(n)) is the WIP quantity between the firstoperation (O₁) and the checked operation (O_(n)), and WPH(o_(n)) is thethroughput rate of the checked operation (O_(n)).
 4. The control systemas claimed in claim 1 wherein the status for each operation is furtherdefined according to a process time for each operation between the firstoperation and the checked operation except that process time attributedto the first operation (O₁) and the checked operation (O_(n)).
 5. Thecontrol system as claimed in claim 4 wherein the status is defined asfollows:S=(WIP(o ₁ ,o _(n))/WPH(o _(n)))−PT(o ₂ ,o _(n−1)), wherein S is thestatus of a subsequent checked operation (o₂˜o_(n−1)) WIP(o₁,o_(n)) isthe WIP quantity between the first operation (O₁) and the checkedoperation (O_(n)), WPH(o_(n)) is the throughput rate of the checkedoperation (O_(n)), and PT(o₂,o_(n−1)) is the total process time ofoperations between the first operation (O₁) and the subsequent checkedoperation (o₂˜o_(n−1)) except that process time attributed to the firstoperation (O₁) and the checked operation (O_(n)).
 6. The control systemas claimed in claim 1 wherein the time constraints comprise overlappingtime constraints.
 7. The control system as claimed in claim 1 whereinthe time constraints comprise a constraint selected from the groupconsisting of dual-operation, multi-operation, and continuous timeconstraints.
 8. The control system as claimed in claim 1 wherein aproduction line is directed to perform related operations if the lot isreleased to the production line.
 9. The control system as claimed inclaim 8 wherein the production line is a production line formanufacturing semiconductor products.
 10. A method for managing aproduction schedule having time constraints that define a maximumelapsed time between operations, comprising the steps of: defining aplurality of sub-time constraints between each two operations;generating plurality of equations according to the time constraints andthe sub-time constraints; calculating the sub-time constraints using theequations; defining a status for each operation according to aWork-In-Process (WIP) quantity between a first operation and a checkedoperation of the production schedule and a throughput rate of thechecked operation; checking whether the status violates the sum of thecalculated sub-time constraints between the first operation and thechecked operation; and releasing a lot if the status for each operationsatisfies the corresponding sum of the sub-time constraints.
 11. Themethod as claimed in claim 10 further comprising simulating at least onequeue time between two operations, and assigning the queue time to oneof the sub-time constraints, thereby obtaining a remnant sub-timeconstraint.
 12. The method as claimed in claim 10 wherein the status isdefined as follows:S=WIP(o ₁ ,o _(n))/WPH(o _(n)), wherein S is the status of a checkedoperation (O_(n)), WIP(o₁,o_(n)) is the WIP quantity between the firstoperation (O₁) and the checked operation (O_(n)), and WPH(o_(n)) is thethroughput rate of the checked operation (O_(n)).
 13. The method asclaimed in claim 10 further comprising defining the status for eachoperation according to a process time for each operation between thefirst operation and the checked operation except that process timeattributed to the first operation (O₁) and the checked operation(O_(n)).
 14. The method as claimed in claim 13 wherein the status isdefined as follows:S=(WIP(o ₁ ,o _(n))/WPH(o _(n)))−PT(o ₂ ,o _(n−1)), wherein S is thestatus of a subsequent checked operation (o₂˜o_(n−1)), WIP(o₁,o_(n)) isthe WIP quantity between the first operation (O₁) and the checkedoperation (O_(n)), WPH(o_(n)) is the throughput rate of the checkedoperation (O_(n)), and PT(o₂,o_(n−1)) is the total process time ofoperations between the first operation (O₁) and the subsequent checkedoperation (o₂˜o_(n−1)) except that process time attributed to the firstoperation (O₁) and the checked operation (O_(n)).
 15. The method asclaimed in claim 10 wherein the time constraints comprise overlappingtime constraints between the operations.
 16. The method as claimed inclaim 10 wherein the time constraints comprise a constraint selectedfrom the group consisting of dual-operation, multi-operation, andcontinuous time constraints.
 17. The method as claimed in claim 10further comprising performing related operations if the lot is releasedto a production line.
 18. The method as claimed in claim 17 wherein theproduction line is a production line for semiconductor products.
 19. Adispatch method that accommodates overlapping time constraints thatdefine a maximum elapsed time between select operations in a productionschedule, comprising the steps of: defining a plurality of sub-timeconstraints between each two operations; generating plurality ofequations according to the time constraints and the sub-timeconstraints; simulating at least one queue time between two operations;assigning the queue time to one of the sub-time constraints; andcalculating a remnant sub-time constraint using the equations.
 20. Thedispatch method as claimed in claim 19 wherein the production scheduleis applied in manufacturing semiconductor devices.
 21. A method formanaging the manufacture of production lots of semiconductor devices,the method operable on a production schedule defining a plurality oftime constraints between corresponding production operations, comprisingthe steps of: defining a plurality of sub-time constraints between eachtwo operations; generating plurality of equations according to the timeconstraints and the sub-time constraints; calculating the sub-timeconstraints using the equations; defining a status for each operationaccording to a Work-In-Process (WIP) quantity between a first operationand a checked operation and a throughput rate of the checked operation;checking whether the status violates the sum of the sub-time constraintsbetween the first operation and the checked operation; releasing a lotof a semiconductor product into a production line when the status foreach operation satisfies the corresponding sum of the sub-timeconstraints; and manufacturing the semiconductor product when the lot isreleased to the production line.
 22. The method as claimed in claim 21further comprising simulating at least one queue time between twooperations, and assigning the queue time to one of the sub-timeconstraints, thereby obtaining a remnant sub-time constraint.
 23. Themethod as claimed in claim 21 wherein the status is defined as follows:S=WIP(o ₁ ,o _(n))/WPH(o _(n)), wherein S is the status of a checkedoperation (O_(n)), WIP(o₁,o_(n)) is the WIP quantity between the firstoperation (O₁) and the checked operation (O_(n)), and WPH(o_(n)) is thethroughput rate of the checked operation (O_(n)).
 24. The method asclaimed in claim 21 further comprising defining the status for eachoperation according to a process time for each operation between thefirst operation and the checked operation except that process timeattributed to the first operation (O₁) and the checked operation(O_(n)).
 25. The method as claimed in claim 24 wherein the status isdefined as follows:S=(WIP(o ₁ ,o _(n))/WPH(o _(n)))−PT(o ₂ ,o _(n−1))), wherein S is thestatus of a subsequent checked operation (o₂˜o_(n−1)), WIP(o₁,o_(n)) isthe WIP quantity between the first operation (O₁) and the checkedoperation (O_(n)), WPH(o_(n)) is the throughput rate of the checkedoperation (O_(n)), and PT(o₂,o_(n−1)) is the total process time ofoperations between the first operation (O₁) and the subsequent checkedoperation (o₂˜o_(n−1)) except that process time attributed to the firstoperation (O₁) and the checked operation (O_(n)).
 26. The method asclaimed in claim 21 wherein the time constraints comprise overlappingtime constraints between the operations.
 27. The method as claimed inclaim 21 wherein the time constraints comprise a constraint selectedfrom the group consisting of dual-operation, multi-operation, andcontinuous time constraints.
 28. The method as claimed in claim 21wherein the step of manufacturing the semiconductor product comprisesperforming related operations thereon.
 29. A semiconductor productproduced according to the method for managing the manufacture ofproduction lots of semiconductor devices of claim
 21. 30. Asemiconductor product produced according to the method for managing themanufacture of production lots of semiconductor devices of claim
 22. 31.A semiconductor product produced according to the method for managingthe manufacture of production lots of semiconductor devices of claim 23.32. A semiconductor product produced according to the method formanaging the manufacture of production lots of semiconductor devices ofclaim
 24. 33. A semiconductor product produced according to the methodfor managing the manufacture of production lots of semiconductor devicesof claim
 25. 34. A semiconductor product produced according to themethod for managing the manufacture of production lots of semiconductordevices of claim
 26. 35. A semiconductor product produced according tothe method for managing the manufacture of production lots ofsemiconductor devices of claim
 27. 36. A semiconductor product producedaccording to the method for managing the manufacture of production lotsof semiconductor devices of claim
 28. 37. A computer-readable mediumcomprising executable instructions for controlling a production scheduledefining a plurality of time constraints between correspondingproduction operations, comprising: computer-readable program code fordefining a plurality of sub-time constraints between each twooperations; computer-readable program code for generating a plurality ofequations according to the time constraints and the sub-timeconstraints; computer-readable program code for calculating the sub-timeconstraints using the equations; computer-readable program code fordefining a status for each operation according to a Work-In-Process(WIP) quantity between the first operation and the checked operation ofthe production schedule and a throughput rate of the checked operation;computer-readable program code for checking whether the status violatesthe sum of the sub-time constraints between the first operation and thechecked operation; and computer-readable program code for releasing alot into the production line if the status for each operation satisfiesthe corresponding sum of the sub-time constraints.
 38. Thecomputer-readable medium as claimed in claim 37 further comprisingcomputer-readable program code for simulating at least one queue timebetween two operations, and assigning the queue time to one of thesub-time constraints, thereby obtaining a remnant sub-time constraint.39. The computer-readable medium as claimed in claim 37 wherein thestatus is defined as follows:S=WIP(o ₁ ,o _(n))/WPH(o _(n)), wherein S is the status of a checkedoperation (O_(n)), WIP(o₁,o_(n)) is the WIP quantity between the firstoperation (O₁) and the checked operation (O_(n)), and WPH(o_(n)) is thethroughput rate of the checked operation (O_(n)).
 40. Thecomputer-readable medium as claimed in claim 37 further comprisingcomputer-readable program code for defining the status for eachoperation according to a process time for each operation between thefirst operation and the checked operation except that process timeattributed to the first operation (O₁) and the checked operation(O_(n)).
 41. The computer-readable medium as claimed in claim 40 whereinthe status is defined as follows:S=(WIP(o ₁ ,o _(n))/WPH(o _(n)))−PT(o ₂ ,o _(n−1)), wherein S is thestatus of a subsequent checked operation (o₂˜o_(n−1)) WIP(o₁,o_(n)) isthe WIP quantity between the first operation (O₁) and the checkedoperation (O_(n)), WPH(o_(n)) is the throughput rate of the checkedoperation (O_(n)), and PT(o₂,o_(n−1)) is the total process time ofoperations between the first operation (O₁) and the subsequent checkedoperation (o₂˜o_(n−1)) except that process time attributed to the firstoperation (O₁) and the checked operation (O_(n)).
 42. Thecomputer-readable medium as claimed in claim 37 wherein the timeconstraints comprise overlapping time constraints between theoperations.
 43. The computer-readable medium as claimed in claim 37wherein the time constraints comprise a constraint selected from thegroup consisting of dual-operation, multi-operation, and continuous timeconstraints.
 44. The computer-readable medium as claimed in claim 37wherein the production line is a production line for semiconductorproducts.
 45. A computer-readable medium for dispatching product lots ina in a production process having a plurality of overlapping timeconstraints between corresponding production operations, comprising:computer-readable program code for defining a plurality of sub-timeconstraints between each two operations; computer-readable program codefor generating plurality of equations according to the time constraintsand the sub-time constraints; computer-readable program code forsimulating at least one queue time between two operations;computer-readable program code for assigning the queue time to one ofthe sub-time constraints; and computer-readable program code forcalculating a remnant sub-time constraint using the equations.
 46. Thecomputer-readable medium as claimed in claim 45 wherein the productionprocess is a production process for manufacturing semiconductorproducts.